A technique of reducing dimension on sequential system of linear equations algorithm for optimization with linear complementary constraints;

We consider a mathematical program with linear complementary constraints (MPLCC).

Equilibrium problem with linear complementary constraints can be reformulated as the solution to a smoothing nonlinear system of equations by means of a complementary function and the smoothing approximation method.

A kind of nonlinear complementarity constraints with equilibrium problems is studied.

A special kind of optimization problems with linear complementarity constraints was studied.

Generator reactive limiter, load tap changing limiter and static var compensator adjust limiter were modeled by nonlinear mixed complementarity constraints and incorporated into the optimization problem to determinate critical point of voltage stability of power systems.

As we know, optimization problems with complementarity constraints have a wide application in economy, engineering design, game theory, making decision and so on, so in recent years there has been a growing literature on these important optimization problems.

The main results are as following: A parameterized equivalent formulation of MPCC is obtained by using the La-grangian multiplier function, and an approach of modifying multiplier with the active-setproperty is presented.